To get an answer would require many more facts, review of the offering, and a better idea of what you want to accomplish and why.
This answer is for informational purposes only and is not legal advice regarding your question and does not establish an attorney-client relationship.
The question, unfortunately, is lacking sufficient facts to give an appropriate answer however, in general, if statements are enough to cause an investor to decide whether or not to purchase securities then they are material. If the material statements misrepresent the offering or the investment then the offeror, or person making the statements, may be liable to the investor for damages incurred in connection with the investment.
I agree that more documents are necessary to give you a definitive answer. I also assume you are asking whether the statement means that the offeror must hire you.
The answer is that the terms of your relationship are governed by your contract with the offeror, and not by the offering. If that contract allows the offeror to terminate you, then the investment offering is unlikely to give you additional rights to remain as the management company.
You need to consult with counsel, however, to be sure as to your specific case.
If your company is listed, the offeror is making a warranty and representation that you are providing certain services, subject to all of the disclosures in the PPM and partnership agreement. The relationship betwen the company offering securities and your own company should be memorialized in a written agreement. If it isn't, you need an agreement ASAP.
The foregoing is not legal advice nor is it in any manner whatsoever meant to create or impute an attorney/client relationship.
It depends on what you're managing.
In any private securities offering, things are going to happen that are unpredictable after the offering closes and, ostensibly, the money gets used in accordance with the use of proceeds described therein.
One concern I would have for you is that, if the investment goes south, to whom will the investors look for satisfaction? The described management company might be a good start.
The securities laws provide remedies for private investors against "material aiders." If you know that your company isn't the management company as described in the memorandum, might you be on notice that the investors were told something that wasn't true?
Might you then also be possessed of an obligation to let those investors know that the offering documents are wrong?
Food for thought.
Remember: I'm not your lawyer, and this is not legal advice. Consult your own attorney.